The answer probably depends on what your utility is nearest to being proportional to the logarithm of.

Most likely your utility (so far as you have one) looks like other_stuff + f(wealth) where wealth = g(annual_income, liquid_assets, other_assets) or something of the kind, where f and g are functions about which we don't know very much. It's probably OK to assume that g is just a linear combination of its inputs. So it seems like there are two things to do.

• Figure out what g looks like by imagining various possible states-of-wealth and ordering them by preference. E.g., would you rather an income of £50k/year and assets of £500k of which £100k are easily accessible, or an income of £200k/year and no assets, or no income and assets of £1M of which £200k are easily accessible? Etc.
• Figure out what f looks like by imagining various gambles. E.g., suppose you have no assets; would you prefer a salary of £30k or of (£25k or £40k, equiprobably)?

And then you can try plugging the result into the Kelly formula, seeing how over-risky it feels, and (if you are so inclined) correcting for excess risk aversion not already factored into f.